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Calculation of Brownian particle transmission in long, wide channels
Author(s) -
Myers Matthew R.
Publication year - 2001
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690470203
Subject(s) - channel (broadcasting) , brownian motion , particle (ecology) , nucleation , transmission (telecommunications) , mathematical analysis , mechanics , physics , mathematics , thermodynamics , quantum mechanics , oceanography , geology , electrical engineering , engineering
The transport of Brownian particles in channels which are long and wide compared to their height is addressed. The cross‐sectional shape of the channel is assumed to be slowly varying, but otherwise arbitrary. A solution to the convective‐diffusive equation with reaction‐rate boundary condition was obtained by locally incorporating the modified Graetz solution in a flat channel. The solution was evaluated asymptotically for the cases of a channel with a maximum height occurring at an endpoint and at an interior maximum. The asymptotic method was applied in two example geometries: the calibration apparatus used to determine reaction‐rate constants for virus adsorption to latex barriers, and overlapping pores in a nucleation‐track membrane. The asymptotic expressions compared well with finite‐element calculations in the examples. The utility of the asymptotic approach lies in rapid estimation of particle transmission through a channel as a function of geometric and physical parameters.